Amplituhedron Solver

Positive-geometry approach to scattering amplitude computation

Overview

A solver built around the amplituhedron formalism, computing scattering amplitudes from positive-geometry structure directly rather than summing Feynman diagrams. Shares a throughline with the Clifford/geometric-algebra work: physics encoded as geometric structure rather than as a sum over terms.

Architecture

• Kinematic data represented in momentum-twistor variables
• Positroid cell decomposition built up via BCFW bridge construction
• Canonical form computed per cell via residue calculus
• Full amplitude assembled as the sum of canonical forms across cells
• Numerical/symbolic backend — likely Python with sympy for exact forms, numerical linear algebra for validation

Milestones

1. 01Implement momentum-twistor kinematics module
2. 02Implement BCFW recursion for tree-level amplitudes (start with MHV, extend to NMHV) as a validation baseline
3. 03Implement canonical form computation for simple positroid cells
4. 04Validate against known analytic tree amplitudes
5. 05Investigate whether the amplituhedron's positive-geometry structure has a genuine Clifford-algebra formulation, or whether the connection to the GW work stays thematic

Open questions

• Scope: stay at tree-level, or eventually reach for loop-level integrands (substantially harder)
• Exact symbolic computation vs. floating-point — precision requirements aren't pinned down yet
• Whether there's a real technical bridge to the Cl(3,0) work or this stays a thematic throughline